Searches for weak spin-dependent forces are commonly interpreted in terms of a basis of sixteen rotationally invariant two-fermion potentials V1−16, including potentials which violate parity (P) and time-reversal (T) invariance. We derive finite-range coordinate-space potentials generated by a massive spin-1 boson with vector, axial-vector, tensor, and pseudotensor couplings to Dirac fermions. In addition to the familiar vector–vector, vector–axial-vector, and axial-vector–axial-vector interactions, we obtain the mixed vector–tensor, vector–pseudotensor, axial-vector–tensor, and axial-vector–pseudotensor potentials, together with tensor–tensor, tensor–pseudotensor, and pseudotensor–pseudotensor terms. We retain the contact terms needed in atomic-scale applications and give compact expressions that include both orderings of inequivalent fermion vertices. We then extend the analysis to a massive spin-2 mediator described by a symmetric Fierz–Pauli field. Besides the conventional coupling to the conserved fermion energy–momentum tensor, we consider a symmetric axial-tensor current. Its nonconservation for massive fermions makes the longitudinal spin-2 helicities contribute to axial-tensor–axial-tensor exchange. The leading minimal spin-2 interactions are either P, T even or P odd and T even; in particular, they do not generate a T-odd potential. Heavy-mediator contact limits and the distinction between the M → 0 massive-spin-2 limit and a genuine massless graviton are also discussed. We map the resulting interactions onto the sixteen-potential Dobrescu–Mocioiu basis and use this mapping to translate existing experimental constraints into numerical limits on spin-1 and spin-2 coupling products in the small- and large-mediator-mass regimes, together with representative limits at finite mediator masses. The derived relations between the boson-exchange coupling constants and the coefficients of the basis potentials also allow published exclusion curves to be rescaled to arbitrary mediator masses.